Oscillations and Waves: An Introduction (Paperback) book cover

Oscillations and Waves

An Introduction

By Richard Fitzpatrick

© 2013 – CRC Press

295 pages | 87 B/W Illus.

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Bridging lower-division physics survey courses with upper-division physics courses, Oscillations and Waves: An Introduction develops a unified mathematical theory of oscillations and waves in physical systems. Emphasizing physics over mathematics, the author includes many examples from discrete mechanical, optical, and quantum mechanical systems; continuous gases, fluids, and elastic solids; electronic circuits; and electromagnetic waves.

Assuming familiarity with the laws of physics and college-level mathematics, the book focuses on oscillations and waves whose governing differential equations are linear. The author covers aspects of optics that crucially depend on the wave-like nature of light, such as wave optics. He also introduces the conventional complex representation of oscillations and waves later in the text during the discussion of quantum mechanical waves. This helps students thoroughly understand how to represent oscillations and waves in terms of regular trigonometric functions before using the more convenient, but much more abstract, complex representation.

Based on the author’s longstanding course at the University of Texas at Austin, this classroom-tested text helps students acquire a sound physical understanding of wave phenomena. It eases students’ difficult transition between lower-division courses that mostly encompass algebraic equations and upper-division courses that rely on differential equations.


Oscillations and waves are ubiquitous in many physical situations. Universities now realise that instead of discussing these phenomena in different branches of physics, it is much more productive to have a core physics undergraduate course which encapsulates the reach physical phenomena such as advection, dispersion, diffraction, as well as non-linearity (solitons, shocks and chaos) in a single, generic course that encompasses the relevant elements of fluid dynamics, mechanics, optics, plasmas and quantum mechanics. There are surprisingly few good and more importantly recent, up-to-date textbooks available on the subject of Oscillations and Waves. Richard Fitzpatrick's Oscillations and Waves: An Introduction is an excellent addition to the existing literature on the subject. The book provides a clear, systematic, comprehensive and yet concise treatment of the subject. The emphasis is placed on physical interpretation rather than mathematical rigour, although the author certainly presents the material at the right mathematical level, commensurate with an advanced undergraduate course. The book will be equally useful for physics and engineering students, as well as mathematics students who want to get physical insight beyond the mathematical equations. The book benefits from very useful exercises which are accompanied by a solutions manual. As a physics educator, I would recommend this book without a reservation to both lecturers as excellent teaching material and to students as a learning resource which will guide them through the exciting world of waves, oscillations and patterns that are all around us.

—David Tsiklauri, Senior Lecturer in Astronomy, School of Physics and Astronomy, Queen Mary University of London, UK

"… The treatment is thorough … An unusual approach of the book is to postpone any use of complex representations until they are needed under the topic of quantum mechanics. The author argues that this allows the text to stress physical interpretations over mathematical solutions. Each chapter includes homework problems. Summing Up: Recommended. Lower- and upper-division undergraduates.

—E. Kincanon, Gonzaga University, in CHOICE Magazine, June 2013

Table of Contents

Simple Harmonic Oscillation

Massona Spring

Simple Harmonic Oscillator Equation

LC Circuits

Simple Pendula

Compound Pendula

Damped and Driven Harmonic Oscillation

Damped Harmonic Oscillation

Quality Factor

LCR Circuits

Driven Damped Harmonic Oscillation

Driven LCR Circuits

Transient Oscillator Response

Coupled Oscillations

Two Spring-Coupled Masses

Two Coupled LC Circuits

Three Spring-Coupled Masses

Transverse Standing Waves

Normal Modes of a Beaded String

Normal Modes of a Uniform String

General Time Evolution of a Uniform String

Longitudinal Standing Waves

Spring-Coupled Masses

Longitudinal Waves on a Thin Elastic Rod

Sound Waves in an Ideal Gas

Fourier Analysis

Traveling Waves

Standing Waves in a Finite Continuous Medium

Traveling Waves in an Infinite Continuous Medium

Wave Interference

Energy Conservation

Transmission Lines

Normal Reflection and Transmission at Interfaces

Electromagnetic Waves

Doppler Effect

Wave Propagation in Inhomogeneous Media

Multi-Dimensional Waves

Plane Waves

Three-Dimensional Wave Equation

Cylindrical Waves

Spherical Waves

Oscillation of an Elastic Sheet

Polarization of Electromagnetic Waves

Laws of Geometric Optics

Fresnel Relations

Total Internal Reflection

Sound Waves in Fluids

Wave Pulses

Fourier Transforms

General Solution of One-Dimensional Wave Equation


Dispersive Waves

Pulse Propagation

Electromagnetic Waves in Unmagnetized Plasmas

Faraday Rotation

Electromagnetic Wave Propagation in Conductors


Pulse Propagation in Two Dimensions

Gravity Waves

Wave Dragon Ships

Ship Wakes

Capillary Waves

Wave Optics


Two-Slit Interference


Multi-Slit Interference

Thin Film Interference

One-Dimensional Fourier Optics

Single-Slit Diffraction

Multi-Slit Diffraction

Two-Dimensional Fourier Optics

Wave Mechanics


Photoelectric Effect

Electron Diffraction

Representation of Waves via Complex Numbers

Schrödinger’s Equation

Probability Interpretation of Wavefunction

Wave Packets

Heisenberg’s Uncertainty Principle

Wavefunction Collapse

Stationary States

Three-Dimensional Wave Mechanics

Particle in Finite Square Potential Well

Square Potential Barrier

Appendix A: Physical Constants

Appendix B: Useful Mathematics

Appendix C: Electromagnetic Theory



Exercises appear at the end of each chapter.

About the Author

Richard Fitzpatrick is a professor of physics at the University of Texas at Austin, where he has been a faculty member since 1994. He is a member of the Royal Astronomical Society, a fellow of the American Physical Society, and the author of Maxwell’s Equations and the Principles of Electromagnetism and An Introduction to Celestial Mechanics. He earned a Master’s degree in physics from the University of Cambridge and a DPhil in astronomy from the University of Sussex.

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Physics
SCIENCE / Solid State Physics